Construction and analysis of an explicit fourth-order symmetric low-regularity integrator for the semilinear Klein-Gordon equation
Year: 2026
Type: preprint
Abstract: In this paper, we propose and analyse a novel explicit fourth-order symmetric low-regularity trigonometric integrator for the semilinear Klein-Gordon equation with non-smooth solution in the $d$-dimensional space, where $d=1,2,3$. The integrator is constructed based on the full use of Duhamel's formula, the employment of a twisted function tailored for trigonometric integrals and the symmetrization procedure of trigonometric integrators. Robust error analysis is conducted, demonstrating that the proposed scheme achieves fourth-order accuracy in the energy space under a weak regularity requirement in $H^{2+\max(μ,1)}(\mathbb{T}^d)\times H^{1+\max(μ,1)}(\mathbb{T}^d)$ with $μ> \frac{d}{2}$. A numerical experiment shows that the proposed low-regularity integrator is much more accurate than some well-known exponential integrators for approximating the Klein-Gordon equation with non-smooth solutions.
Source: arXiv (Cornell University)
Authors: Wang, Bin, Miao, Zhen, Jiang, Yaolin
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2217401733, G8763304138, G9001303705
OpenAlex ID: W7221760544